# Exploring the Relationship Between Moment and Blade Spin Direction in Statics

• vjk2
In summary, the angular velocity unit vector points in the direction of the angular velocity. But there is a convention called the "right hand rule" which says that if you are below the blade, looking up at the whole thing, your extended thumb points in the direction of the angular velocity vector.

#### vjk2

if I spinned a flat blade (eg: no lift) clockwise it should go up, and counterclockwise it should go down in accord with what I've been taught so far about the cross product as it relates to statics. Does this occur?

Off hand this doesn't make sense. But the math seems to suggest it...

vjk2 said:
if I spinned a flat blade (eg: no lift) clockwise it should go up, and counterclockwise it should go down in accord with what I've been taught so far about the cross product as it relates to statics.
Why do you think this?

vjk2 said:
if I spinned a flat blade (eg: no lift) clockwise it should go up, and counterclockwise it should go down in accord with what I've been taught so far about the cross product as it relates to statics. Does this occur?

Off hand this doesn't make sense. But the math seems to suggest it...

I think you might be referring to the angular velocity unit vector. But this doesn't mean that the blade (or any other object) is going to necessarily move in that direction. Rather the direction of angular velocity is merely a convention.

Angular velocity has a direction which is perpendicular to the instantaneous velocity of any point on the object that is actually spinning. In other words, the angular velocity points along the axis of spin. But there still needs to be some convention about which way, along the axis (up or down), the vector points.

There is a convention called the "right hand rule" that says if you put your fingers along the direction of spinning, such that spinning starts at your hand and works its way out to your fingertips, then your extended thumb points in the direction of the angular velocity vector. But this is just a convention.

Hypothetically, the convention could have just as easily been defined using the "left hand rule" such that the angular velocity's direction is always defined using the left hand. If that rule were made instead, and it was consistently also applied to angular acceleration, torque, and everything related, all the final answers would come out the same in the end, although some of the intermediate answers (things still in terms of angular velocity, torque, etc.) might have different signs.

But to ensure that you get the same intermediate answers that your instructor/text book expects, make sure you use the right hand rule (not the left hand rule). Angular momentum, angular velocity, angular acceleration, and torque are all defined using the right hand rule. Just realize that it's nothing more than a well established convention.

(By the way, as you've described it, the right-hand-rule applies to your particular blade analogy, only if you are below the blade, looking up at the whole thing.)

## 1. What is the purpose of exploring the relationship between moment and blade spin direction in statics?

The purpose of exploring this relationship is to understand how the direction of a blade's spin can affect the moment (rotational force) it produces. This knowledge can be applied in various engineering and design fields, such as in wind turbines or helicopter blades, to optimize performance and efficiency.

## 2. How are moment and blade spin direction related in statics?

In statics, the moment produced by a blade is directly proportional to its spin direction. This means that changing the direction of the blade's spin will also change the magnitude and direction of the moment it produces.

## 3. What are the factors that can influence the relationship between moment and blade spin direction?

The relationship between moment and blade spin direction can be influenced by various factors such as the shape and size of the blade, the speed of rotation, and the angle of attack (the angle between the blade and the direction of the wind or fluid flow).

## 4. How can understanding this relationship benefit engineering and design?

Understanding the relationship between moment and blade spin direction can benefit engineering and design by allowing for the optimization of blade designs in various applications. For example, in wind turbines, adjusting the direction of blade spin can help increase efficiency and power generation.

## 5. Are there any real-world applications of this relationship?

Yes, there are many real-world applications of this relationship. Wind turbines, helicopter blades, and propellers are just a few examples where understanding the relationship between moment and blade spin direction is crucial for optimal performance. This relationship is also relevant in fluid mechanics and aerodynamics, which have applications in industries such as aviation and automotive engineering.